Numerical modeling and experimental considerations for a two-coil apparatus to measure the complex conductivity of superconducting films

We consider the accuracy of measurements of the complex conductivity of superconducting films with a two-coil mutual inductance technique. We present a numerical analysis of the procedure by which we deduce the real and imaginary parts of the conductivity, σ=σ1−iσ2, of thin films from the in-phase and out-of-phase components of the mutual inductance of coaxial coils located on opposite sides of the film. The accuracy of the procedure is verified for the full ranges of film radii, thicknesses, and conductivities that are encountered for typical films of a wide variety of cuprate superconductors. We determine both experimentally and theoretically what effect flaws in the film would have on the accuracy of the measurement by examining the effects of holes located at various places in a superconducting film. The effect of capacitive coupling between the coils is measured and shown to be negligible when care is taken in grounding the drive and pickup coil circuits. The mutual inductance of the coils changes wi...